Notes on the p-spin glass studied via Hamilton-Jacobi and Smooth-Cavity techniques

Abstract

In these notes, we continue our investigation of classical toy models of disordered statistical mechanics through various techniques recently developed and tested mainly on the paradigmatic SK spin glass. Here we consider the p-spin-glass model with Ising spins and interactions drawn from a normal distribution N[0,1]. After a general presentation of its properties (e.g. self-averaging of the free energy, existence of a suitable thermodynamic limit), we study its equilibrium behavior within the Hamilton-Jacobi framework and the smooth cavity approach. Through the former we find both the RS and the 1RSB expressions for the free energy, coupled with their self-consistent relations for the overlaps. Through the latter, we recover these results as irreducible expression, and we study the generalization of the overlap polynomial identities suitable for this model; a discussion on their deep connection with the structure of the internal energy and the entropy closes the investigation.

To appear on JMP

References in corpus (6)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• The mean field Ising model trough interpolating techniques
• The infinite volume limit in generalized mean field disordered models
• Irreducible free energy expansion and overlaps locking in mean field spin glasses
• Criticality in diluted ferromagnet
• Positive-Overlap Transition and Critical Exponents in Mean Field Spin Glasses

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